A key difference (aside from the obvious DAM features) is how info about edits is stored.
Ps files, if you use say adjustment layers, stores info in the file. And with layers, that can grow a big file fast. Lr can store in the file, but it adds far less, and adds nothing if you just store the info in Lr's database.
So if you had to say convert a ton of images to BW, crop 'em, correct perspective, and so on, I'd wager each saved Ps file would take up more space than all that editing in Lr. Space is cheap, but still. If I had to convert a couple days of images all with just the kinds of edits one does pro forma (the types of ACR stuff you'd do in Ps) then Lr would just be more efficient at that. So maybe look at it like an ACR alternative vs a Ps alternative.
Start doing things like making virtual copies, and you begin to see why in some situations that's better than saving info in layers or even history in Ps, let alone separate files.
Lr also has publishing, which can be very useful at the end of a workflow. Ps can't maintain the same kind of relationship with exported files as publishing does. Got the same image that needs to go to print in different ways, and for web, and export to send as email, and then you might say hmm, better to do the editing in Lr if at all possible.
These things lend themselves to workflows with lots of images. Yes, Ps can work with batches, and repetitive processes and such, but Lr is designed with that in mind. Kind of fewer edits on more images, while Ps is more edits on fewer images. At least the way I use 'em, but the beauty of them together (and don't forget ugly stepsister Bridge) is that there are many ways of arriving at the same result.
